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Handbook of Mathematical Induction: Theory and Applications (Discrete Mathematics and Its Applications)

Name: Handbook of Mathematical Induction: Theory and Applications (Discrete Mathematics and Its Applications)
Price: 50.75 USD
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3.9 of 5 Stars: Operating Systems - Handbook of Mathematical Induction: Theory and Applications (Discrete Mathematics and Its Applications)

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Book Synopsis: Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics.

In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, transfinite induction, the axiom of choice, Zorn’s lemma, empirical induction, and fallacies and induction. He also explains how to write inductive proofs.

The next part contains more than 750 exercises that highlight the levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. Each self-contained chapter in this section includes the necessary definitions, theory, and notation and covers a range of theorems and problems, from fundamental to very specialized. The final part presents either solutions or hints to the exercises. Slightly longer than what is found in most texts, these solutions provide complete details for every step of the problem-solving process.

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Unlock the power of mathematical induction with the Handbook of Mathematical Induction: Theory and Applications! This indispensable resource lays out a comprehensive guide on how to master the art of writing proofs through mathematical induction. Dive deep into the theory, explore the structure of written proofs, tackle standard exercises, and explore real-world application examples across various mathematical fields. Whether you're a student or a seasoned mathematician, this book is your go-to companion for mastering the art of mathematical induction.

Discover a treasure trove of inductive techniques and explore the world of well-ordered sets, basic mathematical induction, strong induction, and more with Handbook of Mathematical Induction. From ordinals and cardinals to transfinite induction and the axiom of choice, this book covers it all. Learn how to write impeccable inductive proofs and sharpen your problem-solving skills with over 750 exercises of various difficulty levels. Take your mathematical prowess to new heights with this essential guide in your arsenal!

Take your mathematical skills to the next level with Handbook of Mathematical Induction: Theory and Applications. Delve into a wealth of knowledge that will empower you to tackle complex mathematical problems with confidence. From understanding inductive techniques to honing your proof-writing abilities, this book is a must-have reference for anyone seeking to excel in the realm of mathematics. Elevate your understanding of mathematical induction and unlock a world of possibilities with this definitive guide.

Ready to unlock the secrets of mathematical induction and elevate your problem-solving skills? Get your hands on Handbook of Mathematical Induction: Theory and Applications now and embark on a journey to mastery in the world of mathematics!

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